Common fixed points of commuting mappings
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- by William J. Gray and Carol M. Smith PDF
- Proc. Amer. Math. Soc. 53 (1975), 223-226 Request permission
Abstract:
Let $X$ be a dendroid and $S$ an abelian semigroup of continuous monotone self-mappings of $X$. A point $x\epsilon X$ is fixed under $S$ if $g(x) = x$ for all $g\epsilon S$. Let $f:X \to X$ be continuous and commute with each element of $S$. It is shown that $f$ and $S$ have a common fixed point.References
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Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 53 (1975), 223-226
- MSC: Primary 54H25
- DOI: https://doi.org/10.1090/S0002-9939-1975-0377843-1
- MathSciNet review: 0377843